Hysteresis and the hidden rhythm of flow separation and reattachment

Dynamic stall is an unsteady flow phenomenon characterized by the leading edge vortex formation. The formation of the vortex leads to a delay in the flow separation and reattachment and overshoots in aerodynamic forces. The separation delay of a pitching airfoil depends on the effective pitch rate at the critical stall angle, and the separation delay decreases with increasing pitch rate. The current work shows that the reattachment delay follows the same trend if the hysteresis effect is appropriately addressed. The critical reattachment angle should be considered as the reference for estimating the reattachment delay to account for the hysteresis effect. The time constants obtained from separation delay versus pitch rate have previously shown to generalize the Goman-Khrabrov dynamic stall model to predict the flow separation. Here, we test the Goman-Khrabrov model's generalizability for the reattachment stage using the time constants obtained for the reattachment delay.